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Expressing Cardinality Quantifiers in Monadic Second−Order Logic over Trees

Abstract:

We study an extension of monadic second-order logic of order with the uncountability quantifier ``there exist uncountably many sets''. We prove that, over the class of finitely branching trees, this extension is equally expressive to plain monadic second-order logic of order. Additionally we find that the continuum hypothesis holds for classes of sets definable in monadic second-order logic over finitely branching trees, which is notable for not all of these classes are analytic. Our approach...

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Vince Barany More by this author
Lukasz Kaiser More by this author
Alexander Rabinovich More by this author
Publication date:
2010
URN:
uuid:56b6bcf9-5b6a-447b-9478-d257f1b278f7
Local pid:
cs:3583

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